Model-free methods of linkage analysis do not rely on a prior knowledge of the mode of inheritance of a disease and are thus ideal for mapping susceptibility loci for complex diseases. A reparameterization of the affected-sib-pair likelihoods of Risch is proposed. The new parameterization is in terms of variance components and is easily extended to the study of multiple disease loci and their interactions. In addition to the lod score,a test statistic with more power to detect recessive loci is also proposed. Investigation of the use of randomization tests is currently underway.